WATER RESOURCES RESEARCH, VOL. 34, NO. 2, PAGES 213–222, FEBRUARY 1998
Air entrapment effects on infiltration rate and flow instability
Zhi Wang and Jan Feyen
Institute for Land and Water Management, Katholieke Universiteit Leuven, Leuven, Belgium
Martinus Th. van Genuchten
U.S. Salinity Laboratory, USDA-ARS, Riverside, California
Donald R. Nielsen
Department of Land, Air, and Water Resources, University of California, Davis
Abstract. Experiments were conducted to quantify the effects of entrapped air on water
infiltration into a loamy sand. Transparent three-dimensional (3-D) and 2-D columns were
used for experiments carried out for two infiltration conditions: (1) when air was free to
move ahead of the wetting front and leave the bottom of the column (air draining) and
(2) when air was confined ahead of the wetting front and hence could escape only through
the soil surface (air confining). The measurement setup was composed of a tensionpressure infiltrometer, an air flowmeter, water manometers, and video-picture cameras.
We applied both positive and negative water pressures at the soil surface and measured
the simultaneous changes in the rates of water inflow and air outflow, the air pressure
ahead of the wetting front, and the dynamic behavior and advance of the wetting front.
The air pressure ahead of the wetting front for the air-confining condition was generally
found to increase with time rather than reaching a constant level, as observed in other
studies by other researchers. The air pressure fluctuated locally because of air escaping
from the soil surface. On the basis of an analysis of the results we present two empirical
equations to predict the maximum air pressure at which air begins to erupt from the soil
surface and to predict the minimum air pressure at which air eruption stops. We found
that the infiltration rate was always equal to, and controlled by, the rate of air outflow.
The infiltration rate varied inversely with the air pressure ahead of the wetting front and
with the ponding depth at the soil surface. The infiltration rate fluctuated with time rather
than undergoing changes in a three-stage process, as is often characterized in the
literature. The volume of residual entrapped air in the air-confining condition increased
7% on average, and the infiltration rate decreased threefold to tenfold as compared to the
air-draining condition. Finally, it was shown that the air-confining infiltration flow is
fingered and unstable, consistent with the predictions of an existing theory.
1.
Introduction
The movement of water into and through the vadose zone is
in essence a problem of immiscible displacement between air
and water in a porous medium. As water infiltrates into the
vadose zone, soil air is being displaced and may become compressed ahead of the wetting front. Existing laboratory studies
[Wilson and Luthin, 1963; Peck, 1965; Adrian and Franzini,
1966; Latifi et al., 1994] and field experiments [Bodman, 1937;
Dixon and Linden, 1972; Jalali-Farahani et al., 1993] have
shown that soil air compression can lead to a substantial decrease in the rate of infiltration. When the air pressure is
sufficiently high, air will escape from the soil surface, thereby
causing a sharp decrease in air pressure and a major increase
in the rate of water infiltration [McWhorter, 1971; Vachaud et
al., 1974; Touma et al., 1984; Grismer et al., 1994]. Air compression below the wetting front will generally also lead to
residual air entrapment in the transmission zone [Vachaud et
al., 1974; Touma et al., 1984]. An uneven distribution of air
Copyright 1998 by the American Geophysical Union.
Paper number 97WR02804.
0043-1397/98/97WR-02804$09.00
pressure in the subsurface can cause the shallow groundwater
table to decrease or increase locally [Linden and Dixon, 1973].
During periods of intense rainfall, compressed soil air may
break upward through the soil surface, thereby often lifting
and detaching soil particles, leading to increased runoff and
erosion [Jarrett and Fritton, 1978; Suhr et al., 1984].
Although several attempts have been made to mathematically simulate the complex effects of air entrapment on infiltration properties [Morel-Seytoux and Khanji, 1974; MorelSeytoux and Billica, 1985; Parlange and Hill, 1979; Sander et al.,
1988], the underlying physical processes affecting infiltration in
the presence of entrapped air are still not fully understood
conceptually. Also, testing of available theoretical approaches
is seriously hampered by a lack of experimental studies of the
underlying processes. The present study attempts to quantify
the effect of air entrapment on infiltration through a series of
experiments using a dry sand. An experimental setup was designed to measure simultaneous changes in air pressure ahead
of the wetting front, the rate of water inflow, the rate of air
outflow, and the dynamic advance of the wetting front. We
applied both constant (ponded) and variable (suction) pressure heads at the soil surface. The effects of entrapped air on
213
214
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
Figure 1. Experimental setup for simulating the effects of air
entrapment on infiltration. V denotes valves used to refill the
water reservoirs (R 1 and R 2 ) and to control air release from
the soil column.
the hydraulic conductivity and on the onset and extent of
unstable flow (fingering) are also assessed.
2.
Experimental Approach and Materials
The laboratory setup was composed of a soil column, a
tension-pressure infiltrometer, and an air flowmeter (Figure
1). A three-dimensional (3-D) column (cylinder inner diameter
of 8.6 cm and soil height of 45 cm) was constructed of transparent polyvinyl chloride, and a 2-D column (41.5 cm wide, 2.8
cm thick, and with a 50-cm sample height) was constructed of
1-cm-thick transparent acrylic plastic. Both columns were open
at the top and closed at the bottom and sides. Air-confining
conditions were achieved by closing the bottom valve V 5 (Figure 1), and air-draining conditions were achieved by opening
the valve. The soil air pressure was measured 10, 20, 30, and 45
cm below the soil surface using water manometers (ID 5 3
mm). Porous air transmission stones were connected to the
inlet end of each manometer.
We used a modified tension (disc) infiltrometer [Perroux and
White, 1988] to apply both positive pressure heads (ponding)
and suctions (nonponding conditions) at the soil surface. The
traditionally installed disc was replaced in our setup (Figure 1)
with a convex-shaped water supplier to allow air to escape from
the soil surface. Also, the bubbling tube was allowed to move
up and down in the vertical direction. As shown in Figure 1, the
water pressure at the bottom of the water supplier (the infiltration surface) could be regulated by adjusting the height e 1
of the water level in the bubbling tower relative to e 2 , the
vertical distance between the air tube and the water supplier.
When the bubbling tube is set at the baseline defined by e 1 5
e 2 , the pressure at the infiltration surface will be zero. When
e 1 , e 2 , a positive pressure head (ponding) will result,
whereas when e 1 . e 2 , a negative pressure head (suction) will
be imposed at the infiltration surface. When supplying a zero
or negative pressure head at the soil surface, the convex base
was flattened to the soil surface to ensure good contact; however, a 5-mm gap was always maintained between the flattened
water supplier and the column walls to enable the escape of air
from the surface. With such a tension infiltrometer it is also
possible to measure the dynamic air-bubbling (air entry) and
water-bubbling (water entry) values of a porous medium (see
detailed descriptions by Fallow and Elrick [1996]). During our
measurements of the water and air entry values the water
supplier was always completely buried in the sand (instead of
being placed on the surface) to ensure good contact between
the soil matrix and the water supplier.
The air flowmeter consisted of a Marriotte reservoir R 2 and
a spill tube, which discharged water as air entered the reservoir
R 2 . The water exit of the spill tube was set at the same level as
the air inlet tube (with valve V 7 ). A backwater receiver was
placed between the air transmission tube (with valve V 6 ) and
the air flowmeter to receive any possible reverse flow from
reservoir R 2 . This situation will occur when the water level on
the soil surface decreases, thereby creating a vacuum condition
in the headspace of the soil column. At the end of infiltration
under air-draining conditions, air bubbles may be leaving the
bottom of soil columns, together with water. The volumes of
mixed air and water could be separated and measured using
the air flowmeter. The air bubbles would move upward into the
headspace of reservoir R 2 , while the water would leave the
system immediately through the water exit.
Washed, oven-dried sand (4.5% clay, 11.3% silt, and 84.2%
sand) was poured into the transparent 3-D column using a
funnel tube with inside wire screens to randomize the falling
sand. The sand was initially consolidated by first dropping the
sample 200 times from an elevation of 5 cm and subsequently
using a vibrator. The top few centimeters of the sand were
removed to eliminate nonuniformities in bulk density near the
soil surface. The final soil height of the packed samples was 45
cm, and the average bulk density was 1.60 6 0.02 g cm23.
Assuming a particle density of 2.65 g cm23, the total porosity
f 5 0.40 6 0.02. The same packing method was used for the
2-D column. Several experiments using a constant head permeameter [Klute and Dirksen, 1986] indicated that the natural
saturated hydraulic conductivity K s of the sand was 2217 cm
d21 (2.57 3 1024 m s21 or 15.4 mm min21). Air-confining
infiltration tests under constant water heads of 210, 25, 0, 3,
5, 6, 8, and 10 cm and under variable water heads from 210 to
0 cm, 0 to 3 cm, and 0 to 10 cm were conducted. Each experiment was repeated, and the results were compared with those
from the air-draining tests. We used distilled water for all
experiments. A video camera (SONY model CCD-TR808E)
was used to record the development of wetting fronts in the
soil column, the falling water levels in reservoirs R 1 and R 2 ,
and air pressure heads, as indicated in the water manometers.
Images of the wetting front advancement were later digitized
into computer plot files using the ARC/INFO and AutoCAD
hardware and software packages.
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
3.
Experimental Results and Discussion
3.1.
Air Compression Ahead of the Wetting Front
Dynamic changes in air pressure 10, 20, 30, and 45 cm below
the soil surface were measured as water infiltrated into the
sand. Our purpose was to examine the magnitude and distribution of air pressures ahead of the wetting front. Results are
shown in Figure 2.
In the air-draining dry sand column (Figure 2a) the soil air
pressure h a , in excess of the atmospheric pressure, was small
and relatively uniform at all levels ahead of the wetting front.
The value of h a varied between 2 and 4 cm of water. A sharp
wetting front was present, as indicated by very similar values of
the maximum, Z max, and the minimum, Z min, wetting depths.
When the wetting front reached the bottom of the column,
after ;8 min, h a at all levels increased significantly owing to
water intrusion into the manometers.
In the air-confining dry column (Figure 2b), air pressures
ahead of the wetting front initially rose uniformly to a high of
;20 cm at t 5 2 min. At about t 5 7 min and t 5 38 min, soil
air started to erupt from the top, which in turn led to immediate decreases in h a . After t 5 9 min the infiltrating water
submerged the highest air pressure sensor at z 5 10 cm, which
caused the value of h a at this depth to remain at about h a 5
14 cm. The air pressure below the wetting front uniformly
increased to h a . 40 cm. Following the third air eruption at
t 5 38 min, h a rose very abruptly to a maximum value of 47
cm at t 5 55 min. The wetting front was deformed from the
very beginning of infiltration, with a wetting tip (given by Z max)
occupying about half of the circumference of the column wall
and moving much more rapidly than the wetting tail (given by
Z min).
In the air-draining prewetted column (Figure 2c) the sample
was drier at the top but saturated at the bottom. Immediately
upon infiltration, the soil air pressure h a increased at the upper
locations in the column (10, 20, and 30 cm); however, the
bottom air pressure at z 5 45 cm remained zero. Water at the
bottom of the column impeded the air flow. The air pressure
difference between the saturated top layer and the “water
table” at the bottom caused water to flow out of the bottom of
the column. The air pressure at 10 cm remained at relatively
low values (between 10 and 14 cm) owing to submergence of
the air pressure sensor at this level. Air pressures in the middle
of the column (20 –30 cm below the soil surface) generally
increased simultaneously to a maximum of 30 cm, except for
temporary decreases at t 5 0.2, 2, and 5 min when air bubbles
erupted from the top.
As previously noted by Fayer and Hillel [1986], air entrapment can be an important factor in lysimeter studies of infiltration. For example, following the addition of water or a
solute solution to the surface, the air pressure inside the lysimeter may increase, resulting in a near-immediate water discharge from the bottom. The amount of water being then
discharged could be misinterpreted as fluid breakthrough from
the applied water, or a decrease in the water table could be
misinterpreted as direct evaporation from the soil surface.
3.2. Rates of Water Inflow and Air Outflow Under Constant
and Variable Pressure Heads
Air-draining infiltration under a nonponding constant head
h 0 of 210 cm (Figure 3a) resulted in a constant infiltration rate
i w , which was lower than the saturated hydraulic conductivity
K s (15.4 mm min21) of the sand. The air outflow rate i a from
215
Figure 2. Air pressure variation with time in (a) an airdraining dry sand column, (b) an air-confining dry sand column, and (c) an air-draining prewetted sand column. The gage
air pressure h a was measured at depths of 10, 20, 30, and 45 cm
below the soil surface as shown by the h a -10 (squares), h a -20
(circles), h a -30 (diamonds), and h a -45 (triangles) data points,
respectively. Z max and Z min are the maximum and minimum
wetting depths, respectively, and h 0 is the ponding depth on
the soil surface.
the bottom of the column was equal to the water inflow rate i w .
The soil air pressure h a remained constant and close to zero.
When the soil surface was saturated at h 0 5 0 cm (Figure 3b)
at z 5 245 cm (bottom of the column) and h 0 5 10 cm
(Figure 3c), i w and i a were initially much greater than K s but
then slowly approached K s . The soil air pressure remained
close to zero during most of the infiltration period. The abrupt
increase in air pressure at the end of infiltration was caused by
water entry into the water manometer. With air draining from
the bottom the rate of infiltration monotonically increased, and
the total time of infiltration decreased with the increase in h 0 .
Results of the air-confining experiments under constant surface pressure heads are shown in Figure 4, where i a now
indicates the rate of air outflow from the soil surface. When a
negative pressure head h 0 of 210 cm (Figure 4a) was imposed,
both the water inflow rate i w and the air outflow rate i a initially
increased simultaneously. The air pressure h a then remained
equal to zero. After 2 min, h a increased sharply to 10 cm at t 5
4 min, whereas i w and i a decreased abruptly. During the remaining period of infiltration, with h a monotonically increas-
216
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
air escape from the soil surface, i a and i w became identical and
remained relatively small.
The air-confining experimental results revealed pronounced
increases in air pressure h a with increasing h 0 . The maximum
h a attained under the negative pressure head (h 0 5 210 cm,
Figure 4a) was 32 cm of water. Under zero pressure (Figure
4b), h a reached a maximum of 46 cm, while for ponding (h 0 5
10 cm, Figure 4c) h a increased to 49 cm. Contrary to the
results obtained for the air-draining condition (Figure 3), i w
did not monotonically increase with h 0 , nor did i w always
decrease with time. The value of i w appeared to vary inversely
with air pressure h a . Notice that the highest imposed surface
pressure (Figure 4c) resulted in the lowest infiltration rate.
Hence water infiltration into an air-confined medium is negatively affected by the ponding depth on the surface. With air
compression ahead of the wetting front (Figure 4) both i w and
i a were reduced to values much lower than those for the
air-draining condition (Figure 3). For the nonponding condition (h 0 5 210 cm) the time needed to wet the entire sand
column increased almost 4 times, from 18 min (as shown in
Figure 3a) to 70 min (Figure 4a). For the ponding condition
Figure 3. Water inflow rate i w (squares), air outflow rate i a
(circles), and gage air pressure ahead of the wetting front h a
(triangles) as functions of time t for the air-draining condition
under (a) a negative constant pressure source, (b) a constant
zero head, and (c) a constant ponding head.
ing with time at a slower pace, i w and i a remained at a low level
and were equal to each other. Under a zero water head (h 0 5
0, Figure 4b) both i w and i a decreased simultaneously to a
minimum value when h a increased continuously upon infiltration. These results indicate that the soil surface was quickly
sealed by water at the surface, leading to immediate compression of air below the wetting front. After air eruption from the
soil surface at about t 5 2 min, i a and i w increased, while h a
decreased sharply. After 4 min, h a started to increase steadily,
whereas i a and i w decreased again toward zero. The variation
in i w in this case closely resembled the three-phase infiltration
pattern, as described by Christiansen [1944], McWhorter [1971],
and Vachaud et al. [1974]. Christiansen suggested that the
second increase in i w was caused by the gradual dissolution of
entrapped air into the water. However, the results by McWhorter [1971] and Vachaud et al. [1973, 1974], as well as our
experiments, indicate that eruption of compressed air from the
soil surface was the main reason for the increase in i w . For the
ponded condition h 0 5 10 cm (Figure 4c), i w initially decreased, while i a increased starting from zero. After the initial
Figure 4. Water inflow rate i w (squares), air outflow rate i a
(circles), and gage air pressure ahead of the wetting front h a
(triangles) as functions of time t for the air-confining condition
under (a) a negative constant pressure head, (b) a constant
zero head, and (c) a constant ponding head.
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
217
Table 2. Comparison of the Average Water Infiltration
Rate i w in the Air-Confining and Air-Draining Columns
Figure 5. Water inflow rate i w (squares) and gage air pressure ahead of the wetting front h a (triangles) as functions of
time t for the air-confining condition under the ponded variable pressure head h 0 5 0 ; 3 cm.
(h 0 5 10 cm) the required wetting time increased 10 times,
from 5 min in Figure 3c to 48 min in Figure 4c.
Our experiments for a variable surface water head under
air-draining conditions produced almost the same values for
the air pressure and infiltration rate as those obtained with the
constant head experiment (Figure 3), and thus are not further
reported here. However, the varying ponded pressure head
experiment resulted in more abrupt variations in air pressure
h a and the infiltration rate i w . As shown in Figure 5, a slight
decrease in h 0 and h a sometimes triggered substantial jumps in
i w . The jump in i w was especially pronounced when the air
pressure below the wetting front became relatively high (e.g.,
at t 5 23 min). Similar increases in infiltration rate were also
noted in several field plots submerged for long periods of time
[Bodman, 1937; Christiansen, 1944]. A decrease in h 0 may have
suddenly reversed the direction of interfacial air–water displacement (i.e., from a downward displacement of air by water
to an upward displacement of water by air). As a result, the
highly pressurized air suddenly breaks through the soil surface,
thereby causing a major jump in i w . We observed that during
the escape of air bubbles, sand particles also erupted from the
soil surface. The air and sand eruptions created small openings
or holes (2–5 mm in diameter) in the sand surface; this caused
the top layer to become much more loose than the undisturbed
sublayer. Air eruption holes are often observed on sea beaches
at the moment when a sea wave recedes.
We found from the inflow-outflow data that the volumes of
Air-Confining Condition
Air-Draining Condition
Surface
Water
Head
h 0 , cm
Infiltration
Rate i w ,
mm min21
Saturated
Conductivity
K s, %
Infiltration
Rate i w ,
mm min21
Saturated
Conductivity
K s, %
210
25
0
3
5
10
8
9
19
20
20
20
52
58
123
130
130
130
2
3.5
4
5
2
2
13
23
26
32
13
13
water inflow and air outflow for the air-draining condition both
were much greater than the volumes for the air-confining condition (Table 1). This result reflects the greater volume of
entrapped air in the air-confining columns. The average residual air saturation S nw,0 in the air-draining columns was ;20%,
which is comparable to the 19% obtained by Vachaud et al.
[1974] and the 15.6% obtained by Touma et al. [1984]. Residual
air saturation S nw,c in the air-confining condition was 27.3%
on average, very similar to the 23.8% obtained by Vachaud et
al. [1974] and the 26.5% obtained by Touma et al. [1984]. The
data indicate that S nw,c is ;7% higher than S nw,0 . Owing to
the increase in residual air, the hydraulic conductivity in the
wetted region is reduced. The natural saturated water content
for the air-draining condition can be estimated as u s 5 f (1 2
S nw,0 ) 5 0.4(1 2 0.176) 5 0.33. For the air-confining
condition the average water content in the wetted zone was uw 5
f (1 2 S nw,c ) 5 0.278, corresponding to an effective water
content of u * 5 u w u 21
5 0.842. The van Genuchten [1980]
s
estimate (m 5 1 2 n 21 , Table 3) of the relative hydraulic
conductivity k rw in the transmission zone results in k rw 5
u * 1/ 2 [1 2 (1 2 u * 1/m )m] 2 [ 0.4. This indicates that the
hydraulic conductivity during the air-confining condition is reduced by 60% as compared to the air-draining condition.
The water pressure gradient across the transmission zone
also decreased due to the fact that the soil air pressure balances the capillary suction at the wetting front [Grismer et al.,
1994]. Decreases in both the hydraulic conductivity and the
pressure gradient combine to reduce the infiltration rate. The
data in Table 2 indicate the average water inflow rate i w for the
air-draining condition was 3–10 times that for the air-confining
condition. Under the nonponding condition (h 0 , 0), i w
decreased on average from 55% of the saturated conductivity
K s for the air-draining condition to 18% of K s for the air-
Table 1. Comparison of Residual Air Entrapment Following Infiltration Into Air-Draining and Air-Confining 3-D Columns
Air-Draining Columns
Surface
Water Head
h 0 , cm
210
25
0
5
10
Average
Air-Confining Columns
Water
Inflow,
cm3
Air
Outflow,
cm3
Entrapped
Air,
cm3
Residual
S nw,0 ,
%
Water
Inflow,
cm3
Air
Outflow,
cm3
Entrapped
Air,
cm3
Residual
S nw,c ,
%
867
948
892
941
957
816
849
761
862
885
230
197
285
184
161
22.0
18.8
27.2
17.6
15.4
20.2
867
874
860
802
815
788
755
805
727
728
258
291
241
319
318
24.6
27.8
23.0
30.5
30.4
27.3
Residual air saturation is given as a percentage of the total volume of soil pores (1045 cm3 corresponding to the total porosity, f 5 0.4).
218
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
from the soil surface. The water inflow and air outflow rates
changed inversely with air pressure ahead of the wetting front
and with the ponded water depth on the surface. For the loamy
sand the average values of i w and i a were reduced by 70 –90%
as compared to the air-draining condition. Finally, the results
indicate that a minor perturbation in surface water depth may
introduce an immediate and abrupt jump in the rates of air
outflow and water inflow. The immiscible, intermittent displacement between air and water appears to control the process of water infiltration into the vadose zone.
3.3.
Figure 6. Relationships between air pressures, water pressures, and the capillary bubbling (entry) pressures of the sand.
(a) Air pressure h a (triangles), water pressure G 5 h 0 1 Z min
(solid squares), and the capillary pressure h c 5 h a 2 G
(circles), as functions of time t during water infiltration under
h 0 5 2 cm into an air-confining column. (b) Tension infiltrometer data show the changes in soil water pressure h w
(circles). The capillary air-bubbling and water-bubbling pressures h ab and h wb correspond to the average minimum and
maximum values of h w (relative to the atmospheric condition
h a 5 0), respectively. The triangles in Figure 6b indicate
vacuum assistance provided through use of a syringe attached
to valve V 4 in Figure 1 to accelerate the measurement.
confining condition. Values of i w under the ponded pressure
heads (h 0 $ 0) were reduced by a factor of 6, from 128% of
K s for the air-draining condition to 21% for the air-confining
condition. For all pressure heads tested, i w decreased from an
average of 104% of K s for the air-draining condition to an
average of 20% of K s for the air-confining condition. Constantz
et al. [1988] previously found from field experiments with air
entrapment effects that the hydraulic conductivity of the transmission zone remained less than 20% of the saturated conductivity. Our experiments help to explain the dynamic behavior of
infiltration in the field when air entrapment occurs ahead of
the wetting front.
We conclude from the foregoing air-confining experiments
that the entrapped air pressure in the sand generally increases
with time, while fluctuating locally during the entire infiltration
period (i.e., not merely being a three-stage process) as a result
of intermittent air escape from the soil surface. The rates of
water inflow into the soil and air outflow from the soil were
approximately equal after air breakthrough from the soil surface. The rates of water inflow into the soil and air outflow
from the soil were approximately equal after air breakthrough
Air-Breaking and Air-Closing Pressures
Inasmuch as air is compressible the soil air phase should not
be neglected when considering air-water immiscible two-phase
flow. The counterbalancing effects of water pressure and air
pressure at the wetting front control the flux of air and water.
Under air-draining conditions the air phase remains close to
atmospheric pressure and can escape readily at the same rate
as water infiltrates. However, under air-confining conditions,
air is compressed by water. When the air pressure becomes
sufficiently high, the air phase penetrates into the water phase
through large holes created by the air pressure erupting at the
saturated top layer.
The maximum air pressure at which air escapes from a
ponded surface is referred to here as the “air-breaking value”
H b (expressed in water height), whereas the minimum pressure
at which air eruption stops is called the “air-closing value” H c .
We observed that air eruption from the surface started and
stopped rather suddenly. The flow process was highly dynamic
with abrupt increases in the rates of both air outflow and water
inflow. However, flow was relatively static beyond the periods
of air eruption. Immediately before and after air eruption, the
rates of water inflow and air outflow were nearly zero. For an
air bubble to escape from a ponded soil surface the entrapped
air phase must have a sufficiently high air pressure to overcome
the static water pressure, G 5 h 0 1 Z min, above the entrapped air phase at the wetting front (where Z min is the
minimum wetting depth or the thickness of the saturated top
layer). The presence of a saturated top layer had been observed by many researchers in the past; this layer was recently
recognized as being a zone for distribution flow from which
preferential flow seems to emerge [Ritsema et al., 1993]. The
saturated top layer will be slightly desaturated during air eruption through the large air holes. The top layer and air holes
become again saturated after air eruption from the top. A
typical relationship between the compressed air pressure h a
and the water head at the wetting front G is shown in Figure
6a for infiltration under h 0 5 2 cm in an air-confining column.
Also plotted in Figure 6a is the capillary pressure at the airwater interface h c evaluated as the air pressure in excess of G
(i.e., h c 5 h a 2 G). The maximum value of h c , shown by the
peaks of the h c 2 t curve, was nearly constant for a specific
column and varied within a narrow range from 22 to 32 cm for
all columns. The minimum value of h c , shown by the lowest
points of the h c 2 t curve, was also nearly constant for a
specific column and varied within a narrow range from 5 to 18
cm for all columns. According to Youngs and Peck [1964] this
maximum pressure difference h c,max should be equal to the
air-bubbling (air entry) value h ab of a soil. One may similarly
define the water-bubbling (water entry) value h wb of a soil as
the minimum difference h c,min, which is consistent with the
fact that water started to displace air.
Mathematically, h ab and h wb are defined as the inflection
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
points on the main drainage and main wetting retention curves
of the soil, respectively. Assuming van Genuchten’s [1980]
model for the soil water retention curve S e (h), the inflection
point corresponding to d 2 h c /dS 2e 5 0 is located at the point
P(h *c , S *w ) with coordinates
h *c 5
S *e 5
1
a
1
a
F
F
n21
n~m 1 1 2 n 1 1!
12
n21
m~m 1 1!
G
G
m
5
1/n
5
5
S
5
m 1/n
a
m 5 1 2 1/n
1
a
m 5 1 2 2/n
1
11m
D
0.5 m
(1)
Table 3. Optimized van Genuchten [1980] Drainage
Retention Parameters a , m, and n of the Loamy Sand and
the Capillary Pressure h *c and Effective Saturation S *e
Corresponding to the Inflection Point on the Drainage
Retention Curve
van Genuchten
Model Type
a,
cm21
m
n
h *c ,
cm
S *e
m, n Variable
m 5 1 2 2/n
m 5 1 2 1/n
0.091
0.067
0.053
0.158
0.441
0.705
7.866
3.579
3.390
12.67
14.93
17.02
0.80
0.74
0.69
m
m 5 1 2 1/n
m 5 1 2 2/n
(2)
where a , m, and n are drainage retention parameters and S e
is the effective saturation. Physically, the air-bubbling value
h ab is the minimum capillary pressure required for air to enter
the pore network of an initially water-saturated matrix,
whereas the water-bubbling value h wb is the maximum capillary pressure required for water to penetrate into an initially
dry porous matrix [Hillel and Baker, 1988]. Three different
forms of van Genuchten’s [1980] retention model (as shown in
Table 3) gave static air-bubbling values of h ab [ h *c of 13, 15,
and 17 cm, corresponding to effective saturation S *e values of
0.80, 0.74, and 0.69, respectively. As suggested by Corey and
Brooks [1975] the dynamic effects of moving water and air on
the retention curves should be considered when modeling the
infiltration process.
The tension-pressure infiltrometer data for the dynamic airbubbling value h ab and for the dynamic water-bubbling value
h wb of the sand are shown in Figure 6b. The lowest soil water
pressures reflect the dynamic air entry into the initially saturated sand, whereas the highest soil water pressures indicate
water entry into the desaturated soil. The soil water pressure at
air entry was about h w 5 221 cm of water; this dynamic
air-bubbling value should be [Corey and Brooks, 1975, p. 253],
“a few centimeters higher than the static result.” The dynamic
water-bubbling (capillary pressure) value shown in Figure 6b is
approximately h wb 5 9 cm. Note that this value is only slightly
smaller than “one-half of the air-bubbling value,” as suggested
by Bouwer [1966] and Luckner et al. [1989].
The average air-bubbling value h ab and the water-bubbling
value h wb shown in the air-confining infiltration test (Figure
6a) are approximately equal to the values obtained using the
tension-pressure infiltrometer method [Fallow and Elrick,
1996], as shown in Figure 6b. During periods of air pressure
increases (Figure 6a) or soil water pressure decreases (Figure
6b), air breaks into the wetted layer and the soil water retention curve (SWRC) follows a drainage branch toward desaturation of the wetted layer. On the other hand, during periods
when the air pressure decreases (Figure 6a) or the water pressure increases (Figure 6b), the SWRC follows a scanning wetting curve toward resaturation of the sample. We conclude
from the above experimental results that fluctuation in the
entrapped soil air pressure is a result of hysteresis.
Analysis of our experimental results suggests that the following empirical relationships exist for the air-breaking value
H b and the air-closing value H c :
H b 5 Z min 1 h 0 1 h ab
219
(3)
H c 5 Z min 1 h 0 1 h wb
(4)
As reflected in (3) and (4), the maximum and the minimum
entrapped air pressures generally increase when the saturated
top layer (Z min increases) becomes thicker. At the same time,
the air pressures are also subject to changes in the surface
water head h 0 and the air- and water-bubbling values h ab and
h wb of the porous medium. Hence one can predict that if the
capillary pressure h c 5 h a 2 (Z min 1 h 0 ) at the air-water
interface exceeds the air-bubbling value h ab of the porous
medium, air must escape from the soil surface. Conversely, if
h c becomes less than the water-bubbling value h wb of the
material, the top layer will be resaturated. The thickness of the
top layer also increases because the top layer was previously
disturbed by the air eruption paths (cracks or channels), which
lead to a decrease in the water-bubbling value of the top layer.
A lower water-bubbling suction in the top layer allows water to
penetrate into the sublayer.
4. Wetting Front Instability and Preferential Flow
Induced by Air Compression
Several authors [e.g., Raats, 1973; Philip, 1975; White et al.,
1977] previously showed that preferential flow is affected by air
compression ahead of the wetting front. During water infiltration into a sand, gravity fingering dominates the effect of capillary forces [Glass et al., 1991]. Neglecting the viscosity and
density of air with respect to those of water, the original linear
instability criterion [Saffman and Taylor, 1958; Chouke et al.,
1959] can be simplified [Parlange and Hill, 1976] to
iw , Ks
(5)
Thus any time the infiltration rate is less than the saturated
hydraulic conductivity of the porous medium the wetting front
is predicted to be unstable. Assuming an initial sharp wetting
front in the homogeneous sand, i w can also be calculated as
S
iw 5 Ks 1 2
D S
h wf 2 h 0
h af 2 h wb 2 h 0
5 Ks 1 2
L
L
D
(6)
where h wf is the water pressure head immediately above the
wetting front, h af is the gage air pressure immediately below
the wetting front, h wb is the capillary water-bubbling (water
entry) pressure of the medium, and L is the depth of wetting.
Substituting (6) into (5), we obtained an alternative criterion
for predicting the onset of instability at the wetting front:
F 5 h 0 1 h wb 2 h af , 0
(7)
This supplementary criterion is identical to those obtained
previously by Raats [1973] and Philip [1975] using different
220
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
Figure 7. Wetting front advancement in the 2-D column (a) stable flow for the air-draining condition and
(b) unstable flow for the air-confining condition. The arrows in Figure 7b indicate the position of developed
fingers after the wetting front became unstable.
methods. According to (7), instability of the wetting front
could be induced by the following factors or situations, including (1) a decrease in water pressure at the soil surface h 0 or
redistribution of water following infiltration (h 0 becomes negative), (2) a decrease in the water-bubbling value of the porous
media h wb (owing to the occurrence of macropores or the
presence of a fine-textured layer overlaying a coarse-textured
layer), (3) infiltration into hydrophobic media (the value of
h wb is then negative), and (4) an increase in air pressure ahead
of the wetting front h af , a situation being considered in our
study. Diment and Watson [1985] confirmed fingering as caused
by factor 1. Hill and Parlange [1972], Glass et al. [1991], Baker
and Hillel [1990], and Selker et al. [1992] focused on factor 2,
whereas factor 3 was confirmed by Hendrickx et al. [1993] and
Ritsema et al. [1993]. Although White et al. [1977] confirmed
situation 4 with experiments in the Hele-Shaw cells, they were
not successful with soils when the soil air was artificially compressed using a pumping system. From the time when Peck
[1965] noticed “tongues” (fingered flow) in his air-confining
soil columns, few if any systematic studies have been published
on fingering due to natural air compression by infiltrating water.
Our 3-D experiments confirmed that when the instability
criteria of (5) and (7) were satisfied the wetting front becomes
unstable in the initially dry sand. Fingering occurred in all
air-confining columns (Figures 2b, 4a, 4b, 4c, and 5) and also in
the air-draining columns under the negative pressure source
(Figure 3a). Finger development inside the 3-D column was
indicated whenever the maximum wetting front Z max moved
more quickly downward than the minimum front Z min. Results
also indicate that when (5) and (7) are not satisfied the wetting
fronts become stable. A sharp wetting front (Z max 5 Z min)
was maintained during the entire period of infiltration. Stable
flow occurred in all ponded air-draining columns (Figures 2a,
3b, and 3c). The effect of air entrapment on fingering was best
visualized in our 2-D experiments, as shown in Figure 7. For
the ponded air-draining infiltration experiment the wetting
front (Figure 7a) was stable, consistent with the conditions that
i w . K s and F . 0. A sharp wetting front remained present
throughout the infiltration process. However, for the airconfining condition, when both instability criteria were satisfied (i w , K s at t 5 2.5 min and F , 0 at t 5 1 min) owing
to soil air compression, the wetting front became fingered
(Figure 7b) after ;3 min. Repeated experiments, also with
large columns, have shown that the pattern of stable wetting
for the air-draining condition and the pattern of unstable wetting for the air-confining condition were qualitatively reproducible. Random factors arising from the differences in sample
packing and edge effects, and possibly other causes, affected
only the quantitative features of the wetting fronts.
5.
Summary and Conclusions
Infiltration of rainfall or irrigation water over a large surface
area involves water inflow and air outflow, and possibly air
compression. This dynamic process is difficult to observe quantitatively in the field. A laboratory experimental setup consisting of a transparent soil column, a tension-pressure infiltrometer, and an air flowmeter was developed and presented in this
paper. Infiltration experiments under constant and timevarying positive and negative surface water heads, with and
without air compression ahead of the wetting front, were carried out.
The infiltration rate under air-confining conditions generally
fluctuated with time, rather than undergoing changes in a
WANG ET AL.: AIR ENTRAPMENT EFFECTS ON INFILTRATION AND INSTABILITY
three-stage process. When the air pressure ahead of the wetting front reached an air-breaking value, soil air escaped from
the surface, leading to an immediate decrease in the air pressure and an increase in the infiltration rate. When the air
pressure fell below a certain air-closing value, air escape
stopped, the infiltration rate decreased again, and the air pressure increased. This cyclic process repeated itself during the
entire infiltration period, with varying patterns depending on
the stability of the surface water head. A minor decrease in
surface water head was found to lead to an abrupt increase in
infiltration rate. The air-breaking and the air-closing values
were empirically related to the sum of the surface water head,
the depth of the saturated top layer, and the air- and waterbubbling values of the material.
We confirmed experimentally in our 3-D and 2-D columns
that air compression ahead of the wetting front will cause
wetting front instability and flow fingering in a sandy medium.
Although further study is needed to quantify the size and rates
of fingered flow, our results indicate that the effects of the soil
air phase cannot be neglected when modeling infiltration processes.
Macropore flow and fingering in unsaturated field soils are
increasingly being considered as a rule rather than the exception [Flury et al., 1994]. Fingered infiltration may lead to the
accelerated transport of water and nonaqueous phase liquids
toward the groundwater. Fingering also causes an uneven distribution of water and fertilizers in the crop root zone and
increases their degree of leaching to the groundwater table.
Thus further research on flow fingering due to air compression
by infiltrating water, as well as other causes, is of importance
for understanding underlying transport processes in the vadose
zone.
Acknowledgments. This research project was funded by the Katholieke Universiteit Leuven. Comments made by several anonymous
reviewers were greatly appreciated.
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J. Feyen and Z. Wang, Institute for Land and Water Management,
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Belgium 3000. (e-mail: zhi,wang@agr.kuleuven.ac.be)
D. R. Nielsen, Department of Land, Air, and Water Resources,
University of California, 1004 Pine Lane, Davis, CA 95616. (e-mail:
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M. T. van Genuchten, U.S. Salinity Laboratory, USDA-ARS, 450
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(Received July 25, 1997; revised September 29, 1997;
accepted September 30, 1997.)